We further derive an upper bound from the requirement that the magnitude of the first order amplitudes \(a^{(1)}_{(l,m)(l^{\prime },m^{\prime })}\)  (Eq. 14) be much smaller than unity[1]} for results to be valid in first order perturbation. From the above discussion, this implies \(\epsilon \Delta k^2n_1^2<<2k^2n_1(n_1-n_2)/V\) , yielding
\(\epsilon << 2/V.\) 
